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We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive models. We propose two new regularizers based on partial derivatives as nonlinear equivalents of group lasso and elastic net. We formulate the problem within the framework of learning in reproducing kernel Hilbert spaces and show how the variational problem can be reformulated into a more practical finite dimensional equivalent. We develop a new algorithm derived from the ADMM principles that relies solely on closed forms of the proximal operators. We explore the empirical properties of our new algorithm for Nonlinear Variable Selection based on Derivatives (NVSD) on a set of experiments and confirm favourable properties of our structured-sparsity models and the algorithm in terms of both prediction and variable selection accuracy., Comment: Accepted to UAI2018

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction functions that accommodate such non-linearities. The method not only learns the predictive function but also the matrix-valued kernel underlying the function search space directly from the data. Our approach is based on learning multiple matrix-valued kernels, each of those composed of a set of input kernels and a set of output kernels learned in the cone of positive semi-definite matrices. In addition to superior predictive performance in the presence of strong non-linearities, our method also recovers the hidden dynamic relationships between the series and thus is a new alternative to existing graphical Granger techniques., Comment: Accepted for ECML-PKDD 2017

We consider the problem of learning models for forecasting multiple time-series systems together with discovering the leading indicators that serve as good predictors for the system. We model the systems by linear vector autoregressive models (VAR) and link the discovery of leading indicators to inferring sparse graphs of Granger-causality. We propose new problem formulations and develop two new methods to learn such models, gradually increasing the complexity of assumptions and approaches. While the first method assumes common structures across the whole system, our second method uncovers model clusters based on the Granger-causality and leading indicators together with learning the model parameters. We study the performance of our methods on a comprehensive set of experiments and confirm their efficacy and their advantages over state-of-the-art sparse VAR and graphical Granger learning methods., Comment: Changed title plus minor updates in the text